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| Main Authors: | , , , , |
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| Format: | Artículo científico |
| Language: | en |
| Published: |
Physical review. E
2024
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| Online Access: | https://pubmed.ncbi.nlm.nih.gov/39425345/ |
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| _version_ | 1868266290210144256 |
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| author | Abreu, Carlos E P Hermes, Joelson D V da Costa, Diogo Ricardo Medeiros, Everton S Medrano-T, Rene O |
| author_facet | Abreu, Carlos E P Hermes, Joelson D V da Costa, Diogo Ricardo Medeiros, Everton S Medrano-T, Rene O Abreu, Carlos E P Hermes, Joelson D V da Costa, Diogo Ricardo Medeiros, Everton S Medrano-T, Rene O |
| collection | PubMed - marine biology |
| contents | Extreme fractal dimension at periodicity cascades in parameter spaces. Abreu, Carlos E P Hermes, Joelson D V da Costa, Diogo Ricardo Medeiros, Everton S Medrano-T, Rene O In the parameter spaces of nonlinear dynamical systems, we investigate the boundaries between periodicity and chaos and unveil the existence of fractal sets characterized by a singular fractal dimension that deviates greatly from the fractal sets in their vicinity. This extreme fractal dimension stands out from the typical value previously considered universal for these parameter boundaries. We show that such singular fractal sets dwell along parameter curves, called extreme curves, that intersect periodicity cascades at their centers of stability across all scales of parameter spaces. The results reported here are generally demonstrated for the class of one-dimensional maps with at least two control parameters. Generalizations to other classes of systems are possible. |
| format | Artículo científico |
| id | pubmed_39425345 |
| institution | PubMed |
| language | en |
| publishDate | 2024 |
| publisher | Physical review. E |
| record_format | pubmed |
| spellingShingle | Extreme fractal dimension at periodicity cascades in parameter spaces. Abreu, Carlos E P Hermes, Joelson D V da Costa, Diogo Ricardo Medeiros, Everton S Medrano-T, Rene O Extreme fractal dimension at periodicity cascades in parameter spaces. Abreu, Carlos E P Hermes, Joelson D V da Costa, Diogo Ricardo Medeiros, Everton S Medrano-T, Rene O In the parameter spaces of nonlinear dynamical systems, we investigate the boundaries between periodicity and chaos and unveil the existence of fractal sets characterized by a singular fractal dimension that deviates greatly from the fractal sets in their vicinity. This extreme fractal dimension stands out from the typical value previously considered universal for these parameter boundaries. We show that such singular fractal sets dwell along parameter curves, called extreme curves, that intersect periodicity cascades at their centers of stability across all scales of parameter spaces. The results reported here are generally demonstrated for the class of one-dimensional maps with at least two control parameters. Generalizations to other classes of systems are possible. |
| title | Extreme fractal dimension at periodicity cascades in parameter spaces. |
| url | https://pubmed.ncbi.nlm.nih.gov/39425345/ |